Analysis of xx-mith-te3-00088064-base.sdk

Contents

Original Sudoku

level: hard

Original Sudoku

position: 1...56.8....18....6..2.7...27....95.51....4.3......6....1.6.8.77.582.1...6.7.1... initial

Autosolve

position: 1...56.8....18....6..2.7...27....95.51....4.3......6....1.6.8.77.582.1...6.7.1... autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

See Appendix: Full HDP Chains for full list of HDP chains.

Pair Reduction

Pair Reduction

See Appendix: Full HDP Chains for full list of HDP chains.

Deep Pair Reduction

Deep Pair Reduction

Time used: 0:00:11.436886

The following important HDP chains were detected:

* DIS # G2: 2,7 # C2: 3,4,9 => CTR => C2: 2,7
* PRF # G2: 2,7 + C2: 2,7 # C1: 3,4,9 => SOL
* STA # G2: 2,7 + C2: 2,7 + C1: 3,4,9
* CNT   2 HDP CHAINS /  54 HYP OPENED

See Appendix: Full HDP Chains for full list of HDP chains.

Details

Positions

1...56.8....18....6..2.7...27....95.51....4.3......6....1.6.8.77.582.1...6.7.1... initial
1...56.8....18....6..2.7...27....95.51....4.3......6....1.6.8.77.582.1...6.7.1... autosolve
123456789457189236689237541276314958518692473934578612341965827795823164862741395 solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (5)
G3: 3,5
D5: 6,9
E5: 7,9
I4: 1,8
H5: 2,7

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
H3,I3: 1.. / H3 = 1  => 11 pairs (_) / I3 = 1  =>  6 pairs (_)
E4,E6: 1.. / E4 = 1  =>  8 pairs (_) / E6 = 1  => 10 pairs (_)
E4,I4: 1.. / E4 = 1  =>  8 pairs (_) / I4 = 1  => 10 pairs (_)
H3,H6: 1.. / H3 = 1  => 11 pairs (_) / H6 = 1  =>  6 pairs (_)
F5,F6: 2.. / F5 = 2  =>  7 pairs (_) / F6 = 2  =>  9 pairs (_)
B7,C9: 2.. / B7 = 2  =>  7 pairs (_) / C9 = 2  =>  0 pairs (*)
F5,H5: 2.. / F5 = 2  =>  7 pairs (_) / H5 = 2  =>  9 pairs (_)
B7,H7: 2.. / B7 = 2  =>  7 pairs (_) / H7 = 2  =>  0 pairs (*)
B2,B3: 5.. / B2 = 5  =>  5 pairs (_) / B3 = 5  => 12 pairs (_)
D6,F6: 5.. / D6 = 5  =>  5 pairs (_) / F6 = 5  =>  0 pairs (X)
D7,F7: 5.. / D7 = 5  =>  0 pairs (X) / F7 = 5  =>  5 pairs (_)
G9,I9: 5.. / G9 = 5  =>  8 pairs (_) / I9 = 5  =>  6 pairs (_)
D6,D7: 5.. / D6 = 5  =>  5 pairs (_) / D7 = 5  =>  0 pairs (X)
F6,F7: 5.. / F6 = 5  =>  0 pairs (X) / F7 = 5  =>  5 pairs (_)
H2,I2: 6.. / H2 = 6  =>  5 pairs (_) / I2 = 6  =>  6 pairs (_)
C4,C5: 6.. / C4 = 6  =>  7 pairs (_) / C5 = 6  => 10 pairs (_)
D4,D5: 6.. / D4 = 6  => 10 pairs (_) / D5 = 6  =>  7 pairs (_)
H8,I8: 6.. / H8 = 6  =>  6 pairs (_) / I8 = 6  =>  5 pairs (_)
C4,D4: 6.. / C4 = 6  =>  7 pairs (_) / D4 = 6  => 10 pairs (_)
C5,D5: 6.. / C5 = 6  => 10 pairs (_) / D5 = 6  =>  7 pairs (_)
H2,H8: 6.. / H2 = 6  =>  5 pairs (_) / H8 = 6  =>  6 pairs (_)
I2,I8: 6.. / I2 = 6  =>  6 pairs (_) / I8 = 6  =>  5 pairs (_)
C1,C2: 7.. / C1 = 7  =>  6 pairs (_) / C2 = 7  =>  5 pairs (_)
G1,G2: 7.. / G1 = 7  =>  5 pairs (_) / G2 = 7  =>  6 pairs (_)
E5,E6: 7.. / E5 = 7  =>  9 pairs (_) / E6 = 7  =>  7 pairs (_)
H5,H6: 7.. / H5 = 7  =>  7 pairs (_) / H6 = 7  =>  9 pairs (_)
C1,G1: 7.. / C1 = 7  =>  6 pairs (_) / G1 = 7  =>  5 pairs (_)
C2,G2: 7.. / C2 = 7  =>  5 pairs (_) / G2 = 7  =>  6 pairs (_)
E5,H5: 7.. / E5 = 7  =>  9 pairs (_) / H5 = 7  =>  7 pairs (_)
E6,H6: 7.. / E6 = 7  =>  7 pairs (_) / H6 = 7  =>  9 pairs (_)
B3,C3: 8.. / B3 = 8  =>  5 pairs (_) / C3 = 8  =>  8 pairs (_)
I4,I6: 8.. / I4 = 8  =>  8 pairs (_) / I6 = 8  => 10 pairs (_)
A9,C9: 8.. / A9 = 8  =>  5 pairs (_) / C9 = 8  =>  8 pairs (_)
C5,F5: 8.. / C5 = 8  =>  8 pairs (_) / F5 = 8  => 10 pairs (_)
A6,A9: 8.. / A6 = 8  =>  8 pairs (_) / A9 = 8  =>  5 pairs (_)
B3,B6: 8.. / B3 = 8  =>  5 pairs (_) / B6 = 8  =>  8 pairs (_)
* DURATION: 0:00:08.194877  START: 23:00:04.576981  END: 23:00:12.771858 2025-04-04
* CP COUNT: (36)
* SOLUTION FOUND

* DEEP PAIR REDUCTION
* DURATION: 0:00:11.289495  START: 23:00:16.593412  END: 23:00:27.882907 2025-04-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-mith-te3-00088064-base-pr-002.dot
* REASONING
* DIS # G2: 2,7 # C2: 3,4,9 => CTR => C2: 2,7
* PRF # G2: 2,7 + C2: 2,7 # C1: 3,4,9 => SOL
* STA # G2: 2,7 + C2: 2,7 + C1: 3,4,9
* CNT   2 HDP CHAINS /  54 HYP OPENED

Header Info

rating: 22031; r2: 476654; index: 88064

Solution

position: 123456789457189236689237541276314958518692473934578612341965827795823164862741395 solved
Solution

See section Deep Pair Reduction for the HDP chains leading to this result.

Appendix: Full HDP Chains

A1. Pair Reduction Analysis

Full list of HDP chains traversed:

* INC # G2: 3,5 => UNS
* INC # G2: 2,7 => UNS
* INC # B3: 3,5 => UNS
* INC # B3: 4,8,9 => UNS
* INC # G9: 3,5 => UNS
* INC # G9: 2 => UNS
* INC # C5: 6,9 => UNS
* INC # C5: 8 => UNS
* INC # E6: 7,9 => UNS
* INC # E6: 1,3,4 => UNS
* INC # I6: 1,8 => UNS
* INC # I6: 2 => UNS
* INC # H6: 2,7 => UNS
* INC # H6: 1 => UNS
* CNT  14 HDP CHAINS /  14 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # G2: 3,5 => UNS
* INC # G2: 2,7 => UNS
* INC # B3: 3,5 => UNS
* INC # B3: 4,8,9 => UNS
* INC # G9: 3,5 => UNS
* INC # G9: 2 => UNS
* INC # C5: 6,9 => UNS
* INC # C5: 8 => UNS
* INC # E6: 7,9 => UNS
* INC # E6: 1,3,4 => UNS
* INC # I6: 1,8 => UNS
* INC # I6: 2 => UNS
* INC # H6: 2,7 => UNS
* INC # H6: 1 => UNS
* CNT  14 HDP CHAINS /  14 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # G2: 3,5 => UNS
* INC # G2: 2,7 => UNS
* INC # B3: 3,5 => UNS
* INC # B3: 4,8,9 => UNS
* INC # G9: 3,5 => UNS
* INC # G9: 2 => UNS
* INC # C5: 6,9 => UNS
* INC # C5: 8 => UNS
* INC # E6: 7,9 => UNS
* INC # E6: 1,3,4 => UNS
* INC # I6: 1,8 => UNS
* INC # I6: 2 => UNS
* INC # H6: 2,7 => UNS
* INC # H6: 1 => UNS
* INC # G2: 3,5 # H3: 4,9 => UNS
* INC # G2: 3,5 # I3: 4,9 => UNS
* INC # G2: 3,5 # B1: 4,9 => UNS
* INC # G2: 3,5 # D1: 4,9 => UNS
* INC # G2: 3,5 # I8: 4,9 => UNS
* INC # G2: 3,5 # I8: 6 => UNS
* INC # G2: 3,5 # B2: 3,5 => UNS
* INC # G2: 3,5 # B2: 4,9 => UNS
* INC # G2: 3,5 # B3: 3,5 => UNS
* INC # G2: 3,5 # B3: 4,8,9 => UNS
* INC # G2: 3,5 # C5: 6,9 => UNS
* INC # G2: 3,5 # C5: 8 => UNS
* INC # G2: 3,5 # E6: 7,9 => UNS
* INC # G2: 3,5 # E6: 1,3,4 => UNS
* INC # G2: 3,5 # I6: 1,8 => UNS
* INC # G2: 3,5 # I6: 2 => UNS
* INC # G2: 3,5 # H6: 2,7 => UNS
* INC # G2: 3,5 # H6: 1 => UNS
* INC # G2: 3,5 => UNS
* INC # G2: 2,7 # G1: 2,7 => UNS
* INC # G2: 2,7 # G1: 3 => UNS
* INC # G2: 2,7 # C2: 2,7 => UNS
* DIS # G2: 2,7 # C2: 3,4,9 => CTR => C2: 2,7
* INC # G2: 2,7 + C2: 2,7 # G1: 2,7 => UNS
* INC # G2: 2,7 + C2: 2,7 # G1: 3 => UNS
* INC # G2: 2,7 + C2: 2,7 # B3: 3,5 => UNS
* INC # G2: 2,7 + C2: 2,7 # B3: 4,8,9 => UNS
* INC # G2: 2,7 + C2: 2,7 # G9: 3,5 => UNS
* INC # G2: 2,7 + C2: 2,7 # G9: 2 => UNS
* INC # G2: 2,7 + C2: 2,7 # C5: 6,9 => UNS
* INC # G2: 2,7 + C2: 2,7 # C5: 8 => UNS
* INC # G2: 2,7 + C2: 2,7 # E6: 7,9 => UNS
* INC # G2: 2,7 + C2: 2,7 # E6: 1,3,4 => UNS
* INC # G2: 2,7 + C2: 2,7 # I6: 1,8 => UNS
* INC # G2: 2,7 + C2: 2,7 # I6: 2 => UNS
* INC # G2: 2,7 + C2: 2,7 # H6: 2,7 => UNS
* INC # G2: 2,7 + C2: 2,7 # H6: 1 => UNS
* INC # G2: 2,7 + C2: 2,7 # C1: 2,7 => UNS
* PRF # G2: 2,7 + C2: 2,7 # C1: 3,4,9 => SOL
* STA # G2: 2,7 + C2: 2,7 + C1: 3,4,9
* CNT  53 HDP CHAINS /  54 HYP OPENED